Spin waves in quasiperiodic layered ferromagnets

Abstract

We consider a layered ferromagnetic superlattice with spins ${\mathit{S}}_{\mathit{a}}$ and ${\mathit{S}}_{\mathit{b}}$. The exchange energies are ${\mathit{J}}_{1}$ and ${\mathit{J}}_{2}$ between layers, which are arranged in a quasiperiodic Fibonacci sequence, and J in each layer. When ${\mathit{J}}_{1}$=${\mathit{J}}_{2}$=J we use a rescaling approach to obtain an exact decimation transformation for local magnon of layers \ensuremath{\alpha},\ensuremath{\beta},(\ensuremath{\gamma}), and \ensuremath{\delta}(\ensuremath{\tau}) in the ferromagnets. Iteration of the transformation provides numerical results for the local density of states (LDOS) and the magnetization. We found that the bandwidths of the LDOS of layers are the functions of \ensuremath{\eta}=${\mathit{S}}_{\mathit{b}}$/${\mathit{S}}_{\mathit{a}}$.